Consider an aircraft flying in a narrow range of altitudes and slow enough to make air compressibility effects negligible. Then the air density $\rho_{\infty}$ can be considered a constant. For such a case:
1. In steady, level flight, what must happen to the lift coefficient $C_L$ if the flight speed is decreased by a factor of 2? Show how you obtained your answer.
2. All airfoils and wings have a maximum lift coefficient at which they can operate before they experience \"aerodynamic stall.\" An aircraft's wing has a maximum lift coefficient of 2.0, a reference wing area $S = 40\text{ m}^2$, and a take-off weight of 200,000 N. It is taking off at a location where $\rho_{\infty} = 1.2\text{ kg/m}^3$. Find the absolute minimum required take-off velocity. Does this seem like a reasonable answer to you? Why or why not?
3. At the same take-off condition, the moment coefficient about the quarter chord point of the wing ($x/c = 0.25$) is -0.0800 (negative - so a nose-down moment). Find the location of the centre of pressure from the leading edge (non-dimensionalized by chord). The reference length used to define the moment coefficient is the wing chord $c$.
